Expression of type ExprTuple

from the theory of proveit.core_expr_types.tuples

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, f, i, j, k, l
from proveit.core_expr_types import merge_equiv
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, i, j, k, l], Conditional(merge_equiv, And(InSet(subtract(k, i), Natural), InSet(subtract(l, j), Natural), Equals(k, Add(j, one))))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(f, i, j, k, l\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right),f\left(k\right), f\left(k + 1\right), \ldots, f\left(l\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(l\right)\right) \end{array} \end{array} \textrm{ if } \left(k - i\right) \in \mathbb{N} ,  \left(l - j\right) \in \mathbb{N} ,  k = \left(j + 1\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	32, 43, 44, 34, 36
3	Conditional	value: 4 condition: 5
4	Operation	operator: 20 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	ExprTuple	14, 15
10	ExprTuple	16
11	Operation	operator: 18 operands: 17
12	Operation	operator: 18 operands: 19
13	Operation	operator: 20 operands: 21
14	ExprRange	lambda_map: 22 start_index: 43 end_index: 44
15	ExprRange	lambda_map: 22 start_index: 34 end_index: 36
16	ExprRange	lambda_map: 22 start_index: 43 end_index: 36
17	ExprTuple	23, 25
18	Literal
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	34, 26
22	Lambda	parameter: 39 body: 27
23	Operation	operator: 30 operands: 28
24	Operation	operator: 30 operands: 29
25	Literal
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operand: 39
28	ExprTuple	34, 35
29	ExprTuple	36, 37
30	Literal
31	ExprTuple	44, 38
32	Variable
33	ExprTuple	39
34	Variable
35	Operation	operator: 41 operand: 43
36	Variable
37	Operation	operator: 41 operand: 44
38	Literal
39	Variable
40	ExprTuple	43
41	Literal
42	ExprTuple	44
43	Variable
44	Variable